The Risk Premium, Exchange Rate Expectations, and the Forward Exchange Rate: Estimates for the Yen-Dollar Rate

TLDR: In this paper, the forward rate is an unbiased predictor of the future spot rate and the rejection of this hypothesis could occur because market behavior is inconsistent with rational-expectations or because there exists a risk premium.

Abstract: The hypothesis that the forward rate is an unbiased predictor of the future spot rate has been rejected in many empirical studies. The rejection of this hypothesis could occur because market behavior is inconsistent with rational-expectations or because there exists a risk premium. Equations describing the forward premium and the change in the exchange rate are estimated jointly, and tests of both the rationalexpectations and no-risk-premium hypotheses are conducted. Empirical estimates, obtained using quarterly data for the yen‐dollar exchange rate, reject the rational-expectations hypothesis and suggest that there exists a time-varying risk premium.

Figures

Table 3 Tests of the Rational Expectations and No Risk Premium Hypotheses

Table 1 Estimates of the Exchange Rate Forecast Equation General Forecast Model Simple Forecast Model

Table 2

Table 4 Correlation of the Forward Premium with the Predicted Risk Premium and the Forecast Exchange Rate Change

Full text

Munich Personal RePEc Archive
The risk premium, exchange rate
expectations, and the forward exchange
rate: Estimates for the Yen-Dollar rate
Landon, Stuart and Smith, Constance
University of Alberta, Department of Economics
6 April 1999
Online at https://mpra.ub.uni-muenchen.de/9775/
MPRA Paper No. 9775, posted 31 Jul 2008 05:47 UTC

The Risk Premium, Exchange Rate Expectations, and the
Forward Exchange Rate: Estimates for the Yen-Dollar Rate*
Stuart Landon and C.E. Smith
Department of Economics
8-14 Tory Building
University of Alberta
Edmonton, Alberta
Canada T6G 2H4
6 April 1999
Corresponding author:
C. E. Smith
Department of Economics
8-14 Tory Building
University of Alberta
Edmonton, Alberta
Canada T6G 2H4
Phone: (780) 492-5940
FAX: (780) 492-3300
e-mail: csmith@econ.ualberta.ca
*We thank an anonymous referee for helpful comments on an earlier draft of this paper.

The Risk Premium, Exchange Rate Expectations, and the
Forward Exchange Rate: Estimates for the Yen-Dollar Rate
Abstract
The forward rate is often used as the market's prediction of the future spot exchange rate
even though the hypothesis that the forward rate is an unbiased predictor of the future spot rate has
been rejected in a large number of empirical studies using data for different countries and time
periods. The rejection of this hypothesis could occur because market behaviour is inconsistent
with rational expectations or because of the existence of a risk premium. Existing studies test for
one or the other, but not both, of these factors. In this paper, equations describing the forward
premium and the change in the exchange rate are estimated jointly, and tests of both the rational
expectations and no risk premium hypotheses are conducted. The empirical estimates, obtained
using quarterly data for the yen-dollar exchange rate, reject the rational expectations hypothesis
and suggest that there exists a time-varying risk premium.
JEL Classification: F31, G14, G11
Keywords: risk premium, forward exchange rate, forward premium

1
See, for example, Dornbusch (1976), Bilson (1979), Frankel (1979), Driskill (1981),
Obstfeld and Rogoff (1984), Meese (1986), Papell (1989), Krugman (1991), Svensson (1992),
Goldberg (1994), Mark (1995), and Flood, Garber and Kramer (1996).
2
See the surveys of Boothe and Longworth (1986), Froot and Thaler (1990), Engel (1995) and
Lewis (1995).
1
1. Introduction
The assumption of uncovered interest rate parity is widely used in both theoretical and
empirical studies.
1
In conjunction with the covered interest rate parity condition, this assumption
implies that the forward exchange rate is equal to the market's prediction of the future spot
exchange rate. However, the hypothesis that the forward rate is an unbiased predictor of the future
spot rate has been rejected in a large number of studies using data for many different countries and
time periods.
2
Underlying the forward rate unbiasedness hypothesis are the assumptions of no risk
premium and rational expectations, where the latter implies that all information useful in
predicting the exchange rate is incorporated in the forward premium. The rejection of the
unbiasedness hypothesis, as reported in previous studies, indicates that one or both of these
assumptions is not consistent with market behaviour. Which of these assumptions does not hold
has different implications for the foreign exchange market. The rejection of rational expectations
suggests that markets are inefficient while the presence of a time-varying risk premium implies
that changes in macroeconomic variables, such as asset supplies, can alter relative asset yields
even if expectations are rational.
The aim of the analysis presented in this paper is to determine whether the forward rate
unbiasedness hypothesis has been rejected because market behaviour is inconsistent with rational
expectations or because there exists a time-varying risk premium. The existing literature on

3
Canova and Ito (1991) use a VAR model and Hai, Mark and Wu (1997) use the Kalman filter
to generate an exchange rate forecast. Using data for four European countries, Nessén (1997)
combines an estimate of movements of the exchange rate within a target zone with expectations
of changes in the target zone itself.
2
unbiasedness has generally examined the rational expectations hypothesis or the hypothesis of a
time-varying risk premium, but not both. For example, a large portion of the unbiasedness
literature employs empirical tests that are conditional on the assumption that there is no time-
varying risk premium. (See Bilson (1981), Longworth (1981), Fama (1984), and the surveys of
Boothe and Longworth (1986), Froot and Thaler (1990), Lewis (1995) and Engel (1995).)
Another strand of the unbiasedness literature imposes an exchange rate expectations
formation mechanism and then determines whether there exists a risk premium, where the risk
premium is calculated as the difference between the forward premium and the forecast change in
the exchange rate. Studies that employ survey data to obtain an exchange rate forecast include
Froot and Frankel (1989), MacDonald and Torrance (1990), Liu and Maddala (1992), Frankel and
Chinn (1993), Cavaglia, Verschoor and Wolff (1994) and Nieuwland, Verschoor and Wolff
(1998). Studies that use an estimating equation to derive expectations of the future spot exchange
rate include Canova and Ito (1991), Hai, Mark and Wu (1997) and Nessén (1997).
3
While these
studies often find evidence of a time-varying risk premium, they do not attempt to model the risk
premium as a function of observed economic variables. As a consequence, they do not provide
any information on whether movements in the risk premium are systematic, the reasons for these
movements, or the consistency of the calculated risk premium with theoretical models of the risk
premium. In addition, these studies cannot test the cross-equation restrictions that implicitly link
the exchange rate expectations process and the forward premium equation.
A related group of studies addresses some of these issues by examining whether
movements in the risk premium vary systematically with observed economic variables. The

Frequently asked questions

Q1. What are the contributions mentioned in the paper "The risk premium, exchange rate expectations, and the forward exchange rate: estimates for the yen-dollar rate" ?

In this paper, equations describing the forward premium and the change in the exchange rate are estimated jointly, and tests of both the rational expectations and no risk premium hypotheses are conducted. The empirical estimates, obtained using quarterly data for the yen-dollar exchange rate, reject the rational expectations hypothesis and suggest that there exists a time-varying risk premium. 

Q2. What have the authors stated for future works in "The risk premium, exchange rate expectations, and the forward exchange rate: estimates for the yen-dollar rate" ?

MacDonald and Taylor ( 1992 ), in their review of the forward market efficiency literature, note that there is a potential for future research that integrates exchange rate forecasts based on past trends with forecasts based on more fundamental factors. This, plus the finding that the forecast of the change in the exchange rate bears little relationship to the forward premium, suggests that most of the variation in the dollar-yen forward premium results from changes in the risk premium rather than from changes in the expected exchange rate. 

Q3. How many lags of the risk premium variables were initially included in the forward premium estimating?

To capture the possibility of slow adjustment in the risk premium, four lags of the risk premium variables were initially included in the forward premium estimating equation. 

Q4. What is the rational expectations hypothesis rejected for the exchange rate forecast?

The rejection of the rational expectations cross-equation restrictions for the model thatemploys the general exchange rate forecast suggests that information useful in predicting the exchange rate is not being incorporated in the forward premium. 

Q5. What is the reason why the no risk premium hypothesis is rejected?

By reporting both sets of test results it is possible to determine whether, if the no risk premium hypothesis is rejected when the rational expectations cross-equation restrictions are imposed, this rejection occurs because the rational expectations restrictions are inconsistent with the data. 

Q6. Why is the forward rate unbiasedness rejected?

To determine whether forward rate unbiasedness has been rejected due to the presence of a time-varying risk premium or because market behaviour is inconsistent with rational expectations, it is necessary to employ a model that incorporates a time-varying risk premium.